JEE Main 2024 — 4 April, Shift 1 — Question 35

Applying Bernoulli's equation

$\mathrm{P}_{1}+\rho g \mathrm{~h}_{1}+\frac{1}{2} \rho v_{1}^{2}=\mathrm{P}_{2}+\rho g \mathrm{~h}_{2}+\frac{1}{2} \rho v_{2}^{2}$

$\left[h_{1} \& h_{2}\right.$ are height of point from any reference level]

Given $\mathrm{v}_{1}=\mathrm{v}_{2}=0$ (for statement-1) $\therefore \mathrm{P}_{1}-\mathrm{P}_{2}=\rho g\left(\mathrm{~h}_{2}-\mathrm{h}_{1}\right)$

For statement-2: $P_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\frac{1}{2} \rho v_{2}^{2}$

$P_{1}-P_{2}=\frac{1}{2} \rho v_{2}^{2}-\frac{1}{2} \rho v_{1}^{2}$

$P_{1}-P_{2}=\rho g h$

$\implies \rho g \mathrm{~h}=\frac{1}{2} \rho v_{2}^{2}-\frac{1}{2} \rho v_{1}^{2}$

$2 \mathrm{gh}=\mathrm{v}_{2}^{2}-\mathrm{v}_{1}^{2}$